Cracking/Fragmentation of glass - wide range of experimentation with this!

 A good example of original research that can be done in the area of fragmentation/cracking of material, such as glass slides, can be found here. Interesting variations can be done on this in numerous ways. FOr instance, looking at what cracks when there's more than 2 layers of slides could be done. Having the landing object land on different locations of the slide can be done. Hitting on an edge rather than the flat face of the slide could be done. Different sized and shaped slides could be used (circular rather than rectangular, for instance - what happens as boundary conditions are changed? Check out the paper and see if this type of research interests you! It is good experience to have in effectively 'counting' experiments, where one does as many cracked examples as possible, and then categorizes each one by a type or class of cracking - basically one looks to 'measure' the probabilities for each type of cracking pattern to form. Or you can try other materials in a similar manner. 

Get some other ideas for these types of experiments with this article. 

Electron Spin - A good story of how theoretical science & research (physics) evolves

 If you've had high school chemistry, likely you've been introduced to the 4 quantum numbers necessary to understand the structure of the periodic table of elements. One of those four numbers is the "spin" of the electron. Spin has traditionally been thought of in a literal sense, as if every electron spins around some axis like a top. But it is not quite that simple. 

If you are interested in theoretical work, a good Scientific American historical article about electronic spin shows how this work is often done, where a lot of what ifs are asked and explored to try and make sense out of a concept or experimental result or physical observation. It often takes years with many brilliant people thinking about a particular phenomenon, before consensus arises among theorists, and hopefully from that process comes predictions that can be tested experimentally. Already something like spin is showing promise as a contender for quantum computing, and as the article discusses, our universe would not be our universe without electronic spin!